Hierarchical clustering and tree stability

Abstract

Hierarchical clustering via neighbor joining, widely used in biology, can be quite sensitive to the addition or deletion of single taxa. In an earlier study it was found that neighbor joining trees on random data were commonly quite unstable in the sense that large re-arrangements of the tree occurred when the tree was reconstructed after the deletion of a single data point. In this study, we use an evolutionary algorithm to evolve extremely stable and unstable data sets for a standard neighbor-joining algorithm and then check the stability using a novel type of clustering called bubble clustering. Bubble clustering is an instance of associator clustering. The stability measure used is based on the size of the subtree containing each pair of taxa, a quantity that provides an objective measure of a given tree's hypothesis about the relatedness of taxa. It is shown experimentally that even in data sets evolved to be stable for a standard neighbor joining algorithm, bubble clustering is a significantly more stable algorithm.